Unitals and inversive planes |
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Authors: | S G Barwick Christine M O'Keefe |
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Institution: | (1) Department of Pure Mathematics, University of Adelaide, 5005 Adelaide, Australia |
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Abstract: | We show that if U is a Buekenhout-Metz unital (with respect to a point P) in any translation plane of order q
2
with kernel containing GF(q), then U has an associated 2-(q2,q+1,q) design which is the point-residual of an inversive plane, generalizing results of Wilbrink, Baker and Ebert. Further, our proof gives a natural, geometric isomorphism between the resulting inversive plane and the (egglike) inversive plane arising from the ovoid involved in the construction of the Buekenhout-Metz unital. We apply our results to investigate some parallel classes and partitions of the set of blocks of any Buekenhout-Metz unital. |
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